2–3 tree
B-tree of order 3
In computer science, a 2–3 tree is a tree data structure, where every node with children (internal node) has either two children (2-node) and one data element or three children (3-node) and two data elements. A 2–3 tree is a B-tree of order 3. Nodes on the outside of the tree (leaf nodes) have no children and one or two data elements. 2–3 trees were invented by John Hopcroft in 1970.
2–3 trees are required to be balanced, meaning that each leaf is at the same level. It follows that each right, center, and left subtree of a node contains the same or close to the same amount of data.
Definitions
We say that an internal node is a 2-node if it has one data element and two children.
We say that an internal node is a 3-node if it has two data elements and three children.
A 4-node, with three data elements, may be temporarily created during manipulation of the tree but is never persistently stored in the tree.
We say that T is a 2–3 tree if and only if one of the following statements hold:
T is empty.
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